where \(\mu _{X}\) , \(\mu _{\hat{X}}\) , \(\Sigma _{X}\)  and \(\Sigma _{\hat{X}}\)  are the mean and covariance of the reference \(X\)  and synthesised \(\hat{X}\)  images, respectively.
In addition to the SSIM and NIQE metrics, we also used a 1-GP regularizer [1]} designed to force the local statistics of the discriminator gradient to be as close to those of real images. Our claim is that such a regularization strategy results in improving visual quality of the generated images especially for attributes like hair, age, skin colour etc. We worked in the WGAN-GP framework to demonstrate our method. The overall discriminator cost function includes the NIQE function regularizer, the SSIM and the 1-GP regularizer defined as:
